Hamiltonian Reduction of General Relativity and Conformal Unified Theory

TL;DR

This paper applies Hamiltonian reduction to general relativity, proposing a unified model with the Higgs field linked to the metric determinant, leading to new cosmological and particle physics insights.

Contribution

It introduces a gaugeless Hamiltonian reduction method for general relativity and unifies it with the Standard Model via a scalar field related to the metric determinant.

Findings

Unification of gravity and Standard Model interactions.

Proposal of a scalar field as the Higgs modulus.

Implications for cosmology and particle physics, including inflation.

Abstract

We discuss the application of the method of the gaugeless Hamiltonian reduction to general relativity. This method is based on explicit resolving the global part of the energy constraint and on identification of one of the metric components with the evolution parameter of the equivalent unconstrained (reduced) system. The Hamiltonian reduction reveals a possibility to unify General Relativity and Standard Model of strong and electro-weak interactions with the modulus of the Higgs field identified with the product of the determinant of 3D metric and the Planck constant. We give the geometrical foundation of the scalar field, derive and discuss experimental consequences of this unified model: the cosmic Higgs vacuum, the Hoyle-Narlikar cosmology, a $\sigma$-model version of Standard Model without Higgs particle excitations and inflation.